Open Access
Add to BibSonomy
Abstract
A mode-locked laser autocollimator, in which a group of first-order diffracted beams from a grating reflector are detected by an autocollimation unit, has an expanded angle measurement range compared with a conventional autocollimator using a single-wavelength laser source. In this paper, a new optical frequency domain angle measurement method is proposed to increase the visibility of output signal of the mode-locked femtosecond laser autocollimator, which is limited by the overlap of the focused diffracted light spots. The output visibility of a prototype femtosecond laser autocollimator has been increased by the proposed method to approximately 100% over a large range of 21600 arc-seconds.
© 2017 Optical Society of America
1. Introduction
A laser autocollimator [1–3] is an important measuring instrument for noncontact precision angle measurement in a variety of applications such as measurement of tilt error motions of ultra-precision motion stages for nanometrology and nanomanufacturing [4], slope profile or flatness measurement of optical surfaces [5, 6], calibration of angle standards (e.g., polygons, rotary index tables) [7], stabilization of the LIGO-interferometer for the detection of gravitational waves [8], etc. In many applications of angle measurement, autocollimators are required to have good signal qualities in terms of visibility, sensitivity and dynamic detection capability over a certain measurement range.
A laser autocollimator projects a collimated laser beam onto a plane mirror reflector which is mounted on a target of interest. The angle change of the target is measured by detecting the deviation of the reflected beam from the reflector with respect to the axis of the projected beam by an autocollimation unit, which consists of a collimator objective to focus the reflected beam and a position-sensing photodetector placed at the focal plane of the collimator objective to measure the displacement of the focused laser spot. In a laser autocollimator, a charge coupled device (CCD) [9, 10] or a photodiode [11–13] is conventionally employed as the light position-sensing photodetector. The laser autocollimator utilizing CCD can provide a measurement range larger than 1000 arc-seconds [14], while its measurement sensitivity is proportional to the focal length of the collimator objective. For example, in a commercial laser autocollimator, which uses a laser as the light source and a CCD as the photodetector, the focal length of the collimator objective is larger than 1000 mm for achieving a measurement resolution better than 0.1 arc-second [14]. This makes the measurement system bulky and not suitable for the applications of on-line measurement where only a small space between the measurement surface and the autocollimator is permitted. On the other hand, the laser autocollimators utilizing photodiodes have advantages of a compact design and a flexible usage, since the measurement sensitivity can be independent of the focal length of the collimator objective [4, 15]. Meanwhile, its measurement range, which is determined by the size of the focused laser spot, is limited to the order of only 100 arc-seconds [16]. This insufficient measurement range restricts the applications of the laser autocollimators.
With the purpose to expand the measurement ranges of laser autocollimators, the authors have developed a unique laser autocollimator by utilizing a mode-locked laser instead of a single-wavelength laser as the light source, and a diffraction grating instead of a plane mirror as the reflector [17]. In this so-called mode-locked laser autocollimator, a number of specific optical modes with optical frequencies equally spaced by a mode spacing, which is typically larger than the repetition rate [18, 19] of the mode-locked laser, are employed to generate a group of first-order diffracted beams by projecting the collimated laser beam onto the diffraction grating reflector. The reflected first-order diffracted beams are focused as a linear array of light spots over a certain length to be detected by a light position-sensing detector (PD). The output of the PD, which is proportional to the optical intensity of the array of the focused light spots, is varied periodically with respect to the change in the tilt angle of the diffraction grating reflector. Compared with the conventional laser autocollimator in which only a single laser beam is reflected from the plane mirror reflector to form a single focused light spot for detection by the PD, the mode-locked laser autocollimator has an expanded measurement range based on the continuous and periodic output of the PD. The previously developed prototype mode-locked laser autocollimator has been verified to have an expanded measurement range of 11000 arc-seconds [17], which is much larger than that of the conventional laser autocollimators.
In the mode-locked laser autocollimator, the angular separation between each two neighboring first-order diffracted beams, which is determined by the mode spacing of the employed optical modes of the mode-locked laser, is an important factor to determine the performance of the autocollimator [17]. Ideally, it is desired to utilize all the optical modes of the mode-locked laser for achieving the utmost sensitivity of angle measurement subject to the conditions that the optical modes can be separated by the diffraction grating reflector to form the group of the first-order diffracted beams and the linear array of the focused light spots can be distinguished by the PD to generate the continuous and periodic output of the autocollimator with respect to a continuous angle variation of the grating reflector. However, even for a mode-locked femtosecond laser, the repetition rate, which is the minimum mode spacing between the optical modes, is typically on the order of 100 MHz [20, 21] and is too small to be separated in space by a diffraction grating. A Fabry-Pérot cavity [22, 23] is thus used in the mode-locked laser autocollimator to filter the optical modes [17]. The mode spacing of the transmitted optical modes, called the effective repetition frequency, can be enlarged to the free spectral range (FSR) of the Fabry-Pérot cavity. Because the FSR can be much larger than the repetition rate of the mode-locked laser, the transmitted optical modes can be employed for the mode-locked laser autocollimator. The effectiveness of this technique for the mode-locked laser autocollimator has been demonstrated by using the Fabry-Pérot cavities with FSRs larger than 100 GHz. In this technique, for a certain FSR, the finesse of the Fabry-Pérot cavity must be low enough so that the adjacent light spots focused on the sensitive area of the PD can have a long enough overlapping length with each other for the array of the focused light spots to have a continuous intensity distribution and the autocollimator to have the continuous and periodic output. However, the overlapping of the light spots can significantly increase the minimum value of the output signal, resulting in a reduction in the visibility of the output signal as well as the measurement sensitivity of the autocollimator. Although efforts had been made to improve the output visibility, only a maximum output visibility of 0.50 was achieved with a complicated double-reflection configuration [17]. It should be noted that, in the previous mode-locked laser autocollimator, the conventional PD-based detection method was employed, which can only detect the overall intensities of the light spots focused on its sensitive area even though the light spots are corresponding to the optical modes with different optical frequencies. This is the fundamental reason for the limited output visibility of the previous mode-locked laser autocollimator.
A new method, which is referred to as the optical frequency domain angle measurement method, is thus proposed in this paper to improve the output visibility as well as the sensitivity of the mode-locked laser autocollimator. Taking into consideration each of the first-order diffracted beams has a determinate and unique optical frequency, the corresponding light spot on the focal plane of the collimator objective can be completely distinguished and separated from the other light spots by detecting the light intensity over the optical frequency domain with an optical spectrum analyzer, even if the light spots are overlapped with each other in the space domain. As a result, the output visibility of the mode-locked laser autocollimator can be theoretically improved to 100% by this method. After a description of the measurement principle, the experimental results with a prototype femtosecond mode-locked laser autocollimator are presented for demonstrating the feasibility of the proposed method.
2. Principle and simulation
A schematic of the femtosecond mode-locked laser autocollimator, compared with a conventional laser autocollimator, is shown in Fig. 1. A mode-locked femtosecond laser, whose spectrum consists of a comb of optical modes with optical frequencies equally spaced by the repetition rate, is employed as the measurement laser source. The femtosecond laser is collimated by a collimating lens (CL) and projected onto a diffraction grating reflector mounted on a target of interest after passing through a Fabry-Pérot cavity for repetition rate multiplication to the free spectral range (FSR) of the cavity. According to the diffraction theory, each of the first-order diffracted beams from the grating reflector has a determined diffraction angle, depending on the frequency of the corresponding optical mode. The group of the first-order diffracted beams are collected and focused by a collimator objective. Compared to the limited measurement range of the conventional laser autocollimator in which only a single reflected beam can be detected, in the femtosecond laser autocollimator, the tilt angle of the grating reflector can be measured with a large measurement range by detecting the group of the first-order diffracted beams with a position-sensing photodetector. The measurable angular range, which is the difference of the diffraction angles between the first and the last first-order diffracted beams, is determined by the spectral range of the laser. The angle interval between the ith first-order diffracted beam corresponding to the ith optical mode with optical frequency vi and the i + 1th first-order diffracted beam corresponding to the i + 1th optical mode with frequency vi+1 can be expressed by:
where βi is the diffraction angle of the laser beam of the ith optical mode, cair is the light speed in air, p is the period of the diffraction grating reflector, n is the number of the optical modes.
Fig. 1 Schematic of the femtosecond laser autocollimator by utilizing a mode-locked femtosecond laser compared with that of a conventional laser autocollimator.
Detection of the group of the first-order diffracted beams by the photodetector is important for the performance of the femtosecond laser autocollimator. Figure 2 shows a schematic of the output of the femtosecond laser autocollimator with respect to the tilt angle variation of the grating reflector when using a PD as the photodetector under different cases of the spectrum of the femtosecond laser modulated by the Fabry-Pérot cavity. The output of the femtosecond laser autocollimator is represented by that of the PD whose output is proportional to the overall intensity of the first-order diffracted beams focused on its sensitive area. As a metric of the signal quality, the visibility Vvisibility of the femtosecond laser autocollimator output is defined as:
where Imax_i and Imin_i are the maximum and minimum output values of the autocollimator, respectively, corresponding to the ith optical mode of the femtosecond laser.Fig. 2 Schematics of the output of the femtosecond laser autocollimator when utilizing a PD as the detector under different spectrum of the laser: (a) without modulation; (b) modulated by a cavity with a small FSR and a low finesse; (c) modulated by a cavity with a large FSR and a low finesse; (d) modulated by a cavity with a large FSR and a high finesse.
As can be seen in Fig. 2(a), if the femtoseond laser has insufficient mode spacing, it cannot be used in the autocollimator for angle measurement since the focused first-order diffracted light spots are difficult to be distinguished by any existing detectors including the PD. Now we assume the case in which the mode spacing of the femtosecond laser is increased by the Fabry-Pérot cavity to a level that the focused light spots corresponding to the transmitted optical modes in the modulated femtosecond laser can be distinguished by the PD, but still with overlaps from each other as shown in Fig. 2(b). In this case, the femtosecond laser autocollimator can be used to make angle measurement with continuous output, but both the output visibility and the measurement sensitivity are low. If the separations of the focused light spots are further enlarged by using a Fabry-Pérot cavity with a larger FSR but a low finesse as shown in Fig. 2(c), the output visibility can be improved from the case shown in Fig. 2(b). However, low sensitivity measurement areas exist at the locations of those focused light spots with poor light intensities corresponding to the filtered optical modes which cannot be fully suppressed by the Fabry-Pérot cavity due to the low finesse. Even if a Fabry-Pérot cavity with a large FSR and a high finesse can be employed to make sufficient suppression of the filtered optical modes as shown in Fig. 2(d), it is still not good for the performance of the autocollimator because detection blind areas will be thus induced among the separated focused light spots and make the output of the autocollimator discontinuous. From the above several cases, it can be seen that based on the conventional detection method, it is difficult for the femtosecond laser autocollimator to synchronously have a satisfied output visibility as well as continuous detection capability over a large measurement range. Since the influence of the filtered optical modes as the cases shown in Figs. 2(c) and 2(d) should be avoided for the sake of angle measurement with sufficient light intensities and continuous detection capabilities, the consideration is focused on an issue that how to keep the advantage of the case as Fig. 2(b) in which the overlapped first-order diffracted beams with sufficient light intensities, corresponding to the transmitted optical modes in the modulated femtosecond laser, are employed for the angle measurement, while the output visibility and the measurement sensitivity can be improved without the influence of the overlap of the diffracted beams.
In responding to this problem, a frequency domain angle measurement method is proposed. As shown in Fig. 3, the focused first-order diffracted beams with overlaps, as that shown in Fig. 2(b), are detected by an optical spectrum analyzer (OSA) through a fiber connection instead of detection with a PD. Since the focused first-order diffracted beams have determined optical frequencies as those of the corresponding transmitted optical modes which are spaced by the repetition rate over the spectrum of the modulated femtosecond laser, the output curve of each first-order diffracted beam with respect to the angle variation of the grating reflector can thus be clearly distinguished with a high visibility in the frequency domain by the OSA on the condition that the frequency resolution of the OSA is smaller than the mode spacing of the femtosecond laser. As shown in the figure, by utilizing this method, the output of the femtosecond laser autocollimator provides a special three-dimensional (3D) observation which is different from the two-dimensional (2D) observation in the conventional laser autocollimator. In the 3D output observation shown in the figure, the X-axis represents the angle variation of the grating reflector, the Y-axis indicates the optical frequency of the first-order diffracted beam, and the Z-axis represents the light intensity of the focused beams received by the OSA. The YZ view corresponds to the frequency domain which is represented by the optical spectrum of the modulated femtosecond laser. Assume the grating reflector has an angular motion for the OSA to receive the group of the focused first-order diffracted beams one by one from the first beam with an optical frequency of v1 to the last beam with an optical frequency of vn, the light intensity received by the OSA varies periodically with the tilt angle variation of the grating reflector. The output of the femtosecond laser autocollimator consists of a number of curves, each of which is corresponding to each of the first-order diffracted beams. In the frequency domain, the output curves are distinguished with the spacing equal to the mode spacing of the modulated femtosecond laser. In the XZ view, the output curves have gradually shifted one by one with respect to the tilt angle change of the grating reflector, in which the shift amplitude in the angle variation axis (X-axis) is equal to the angular interval of the first-order diffracted beams. In this way, unlike the conventional detection method which suffers from low visibility influenced by the overlapped diffracted beams, the optical frequency domain angle measurement method provides a possibility to obtain good visibility over a large measurement range without compromising the continuous detection capability.
Fig. 3 Principle of the optical frequency domain angle measurement method associated with the femtosecond laser autocollimator.
A simulation of the proposed optical frequency domain angle measurement method is carried out. In the simulation, the femtosecond laser is set to have a central frequency of 193 THz and a repetition rate of 100 MHz. The FSR of the Fabry-Pérot cavity is set to be 100 GHz. For the sake of simplicity, the finesse of the cavity is set to be infinite. The diameter of the incident femtosecond laser beam is set to be 3.0 mm and the focal length of the collimator objective is 15.37 mm. The diffraction grating reflector is set to have a grating period of 1.05 μm. The total light intensity of the incident femtosecond laser is set to be 1. Taking into consideration that the purpose of this simulation is only to demonstrate the feasibility of distinguishing the output curve by the differences of their corresponding optical frequencies, the intensity of each optical mode of the femtosecond laser was set to be constant and the chromatic aberration effect of the collimator objective by which the different wavelengths will be focused on slightly different focal planes was not considered for the sake of simplicity. Figure 4 shows a part of the simulation result over a tilt angle variation range of 2100 arc-seconds around the first-order diffracted beam corresponding to the optical mode at the central frequency. As can be seen in the figure, the visibility of the output of the femtosecond laser autocollimator based on the conventional method, which utilizes a PD to detect the overall intensity of the focused first-order diffracted beams on its sensitive area, is only 5.1%. On the contrary, the output based on the optical frequency domain measurement method, by which the output curves are distinguished according to the optical frequencies of the first-order diffracted beams, can be up to 100% that is much higher than the conventional method.
Fig. 4 Simulation result of the output of the femtosecond laser autocollimator by the optical frequency domain measurement method compared with the conventional method.
3. Experiments
A prototype of the femtosecond laser autocollimator with the optical frequency domain angle measurement method was constructed and experiments were carried out to demonstrate the feasibility of the proposed method. Figure 5 shows a schematic of the experimental setup. A collimated laser beam from a femtosecond laser generator (C-Fiber 780 HP, MenloSystems GmbH) was employed as the measurement light source. The femtosecond laser had a central wavelength of 1560 nm and a repetition rate of 100 MHz. The spectral width of the femtosecond laser was 35 nm. The repetition rate of the femtosecond laser was modulated by using a Fabry-Pérot cavity with a FSR of 100 GHz and a finesse of 208. After passing through the cavity, the collimated femtosecond laser was projected onto a diffraction grating reflector mounted on an air-bearing spindle with the angle of incidence of approximately 23.3 degrees. The grating period of the diffraction grating reflector was 1.05 μm. The spindle had a rotational resolution of 0.0038 arc-second measured by an embedded rotary encoder. A series of the first-order diffracted beams from the grating reflector was focused by a collimator objective mounted on a fiber alignment stage. The focal length of the collimator objective was 15.37 mm. The focused first-order diffracted beams were received by a single-mode optical fiber and detected by an optical spectrum analyzer (OSA). The OSA covered a wavelength ranging from 600 nm to 1700 nm and had a wavelength detection resolution of 0.02 nm. The dynamic range of the OSA was 60 dB. It should be noted that since the focus of this paper was to propose and verify the feasibility of the optical frequency domain angle measurement method, for the sake of simplicity, the oscillator of the femtosecond laser was operated at free-running condition. In future application of this method, the femtosecond laser can be locked to a frequency standard such as a Rubidium oscillator for frequency stabilization. Here, for the purpose of not losing the focus of the paper, a commercially-available general-purpose OSA was employed in the verification experiments. It should be noted that the cost of a measuring instrument is an important issue for practical applications, and should be taken into consideration in the next step of instrumentation and engineering work based on the proposed method. It should also be noted that the usage of the OSA and the femtosecond laser generator will not influence the size of the optical head of the autocollimator, because they can be placed at outward positions and can be connected to the head of the autocollimator through the single mode fibers.
Figure 6 shows a two-dimensional (2D) profile and a three-dimensional (3D) profile of the first-order diffracted beams detected by using a beam profiler (BP209-IR/M, Thorlabs). It can be seen that each different first-order diffracted beam could not be distinguished from the observation of the beam profiler, which indicated that the first-order diffracted beams had serious overlaps among each other. It was thus difficult to be employed for angle measurement by using the conventional method. On the other hand, Fig. 7 shows a part of the measurement result based on the proposed optical frequency domain angle measurement method. The measurement range shown in the figure was 432 arc-seconds. As can be seen in the figure, although the group of the first-order diffracted laser beams could not be separated in space, in the frequency domain, the output curves corresponding to each of the focused first-order diffracted beams with respect to the change in the tilt angle of the grating reflector were successfully distinguished, which provided a full output visibility of 100% for the angle measurement. Within the measurement range shown in the figure, there were five output curves in total detected by the OSA located at the frequencies of 199.875 THz, 199.975 THz, 200.075 THz, 200.175 THz and 200.275 THz, respectively. The frequency spacing of the output curves in the frequency domain was 100 GHz, which was the same as the repetition rate of the modulated femtosecond laser. The mean angular interval between the apexes of the output curves was evaluated to be approximately 110 arc-seconds. It should be noted that differing from the simulation results, in which a constant intensity was set for all of the optical modes, the light intensity amplitudes of the output curve at different optical frequencies were not constant in the experiment because each of the optical modes of the femtosecond laser had light intensity different with each other. In addition, although the intensity variation could also be influenced by the chromatic aberration of the collimator objective, this can be eliminated by employing a collimator objective well corrected in terms of the chromatic aberration.
Fig. 6 Intensity distribution of the group of the first-order diffracted beams measured by a beam profiler.
Fig. 7 Output of the femtosecond laser autocollimator by the optical frequency domain measurement method.
Experiments were then extended to a wide measurement range. For reducing the experiment time and the number of the measured data for the sake of simplicity, instead of continuous rotation and sampling, the spindle was controlled to rotate from 0.0 degree to 6.0 degree by 6 large steps of 1.0 degree, and at each large step, it was rotated 0.12 degree by 40 small steps of 0.003 degree. Figure 8 shows the measurement results by the femtosecond laser autocollimator at the angular positions from 0.0 degree to 6.0 degree. It can be seen that over a wide measurement range of 21600 arc-seconds, all of the output curves could be clearly distinguished by the classification of optical frequencies and the output visibilities were always kept to be as full as 100%. The gray dash line in each figure represents the total intensity output detected by the traditional method. From Figs. 8(a) to 8(g), the output visibilities by the conventional detection method were evaluated to be 80.9%, 85.1%, 81.4%, 79.1%, 80.6%, 50.2% and 38.5%, respectively. The visibility variation by the conventional method was due to the different angular separation of the first-order diffracted beams at different spectrum location of the femtosecond laser. The comparison of the output visibility by the optical frequency domain angle measurement method and the conventional method was summarized in Fig. 9. As can be seen in the summarized results shown in Fig. 9, the output visibilities of the femtosecond laser autocollimator have been increased from the level of 0.4 - 0.8 by the conventional detection method to a constant value at 1.0 over the entire measurement range by proposed optical frequency domain angle measurement method.
Fig. 8 Measurement results in a wide range with the frequency domain measurement method at each spindle angular position: (a) 0°; (b) 1°; (c) 2°; (d) 3°; (e) 4°; (f) 5°; (g) 6°.
Fig. 9 Comparison of the visibility by the frequency domain measurement method and that by the traditional method.
In addition, the angle measurement stability by the femtosecond laser autocollimator was also evaluated. Figure 10(a) shows the intensity stability of the first-order diffracted beam corresponding to the optical mode at the central wavelength of 1560 nm over a time of 15 seconds. The peak-to-valley (PV) deviation and the standard deviation of the light intensity were evaluated to be 6.40 nW and 0.88 nW, respectively. The FFT analysis of the intensity stability is shown in Fig. 10(b). The dominating frequencies were mainly below 100 Hz, the root causes of which were considered to be the mechanical vibration of the experimental setup and the influence from the air. Figure 11 shows the angle measurement stabilities corresponding to each of the detected optical modes in Fig. 8, which were calculated from the PV deviation and standard deviation of the light intensities, respectively. The minimum measurement stability, which was located at the optical mode with a frequency of 199.97 THz, was evaluated to be 0.03 arc-second based on the calculation by the standard deviation. This shows that the system is possible to have a potential minimum measurement resolution on the order of 0.03 arc-second. However, detailed analysis and experimental verification of the measurement resolution and accuracy should be further carried out in the future work. In addition, as can be seen in the figure, the measurement stabilities varied at each optical frequency. This was due to the frequency and intensity instability of the optical modes of the femtosecond laser used in the autocollimator. Although the mode-locked femtosecond laser could be phase-locked to a frequency standard such as an atomic clock for a superior frequency and intensity stability, the Fabry-Pérot cavity could still induce additional influences on the stability of the angle measurement results. Some available techniques for stability analysis and stabilization of the Fabry-Pérot cavity such as the Pound-Drever-Hall (PDH) method [23, 24] could be employed for achieving better performances of the autocollimator. Taking into consideration that the primary motivation and focus of this paper is on the proposal and verification of the frequency domain angle measurement method for improvement of the output visibility of femtosecond mode-locked laser autocollimator, analysis and improvement of the measurement stability will be carried out in the future work.
Fig. 10 Stability of the light intensity of the optical mode at the central wavelength: (a) stability of the light intensity; (b) FFT analysis of the stability.
The angle measurement sensitivities, with comparison between the traditional detection method and the proposed optical frequency domain angle measurement method, were also evaluated by taking the measurement result shown in Fig. 8(g) corresponding to first-order diffracted beams with optical frequencies of 203.3 THz, 203.4 THz and 203.5 THz. Figure 12 shows the sensitivity evaluation results. The sensitivities were evaluated by calculating the slope at the locations of A, B and C marked in figure. For the traditional method by detecting the overall intensity output as plotted by the gray dash lines in the figure, the measurement sensitivities for the locations A, B and C were evaluated to be 3.16 × 10−7 mW/arc-second, 3.87 × 10−7 mW/arc-second and 3.07 × 10−7 mW/arc-second, respectively. It should be noted that since the capability of the OSA in detecting small light intensity was higher than that of an ordinary PD, the measurement sensitivities can be much lower in the conventional laser autocollimator than the above evaluated values. On the other hand, with the proposed optical frequency domain angle measurement method, the measurement sensitivities at locations of A, B and C were improved to be 3.54 × 10−7 mW/arc-second, 4.06 × 10−7 mW/arc-second and 3.60 × 10−7 mW/arc-second with improvement percents of 11.2%, 10.5% and 11.7%, respectively, compared to those by the traditional method (see Table 1).
Table 1. Comparison of sensitivities by traditional method and the proposed method.
It should be noted that here we only demonstrated the improvement of the sensitivity by simply using the individual optical frequency domain output at each location, without considering the interactions of the neighboring outputs, for the sake of clarity in the comparison. In addition, since the main focus of this paper is on the proposal and verification of the optical frequency domain angle measurement method for improving the visibility of the output signal of the femtosecond mode-locked laser autocollimator, a Fabry-Pérot cavity with a relatively large FSR and a relatively small finesse was employed in the experiment, which was sufficient for the purpose of verifying feasibility of the proposed method in visibility improvement. For this reason, the angular pitches of the frequency domain outputs of the mode-locked laser were relatively large and the variation of each of the output with respect to the tilt angle variation was relatively smooth. This is why the improvement in the sensitivity and resolution shown in the experiment was not much significant. However, in principle, the sensitivity and resolution can be significantly improved by using a Fabry-Pérot cavity with a small FSR and/or a large finesse. The sensitivity can also be further improved by taking use of the relationship between the multiple optical frequency domain outputs with a 100% visibility of the femtosecond mode-locked laser autocollimator. As a consequence of the improvements in the visibility and sensitivity, the resolution can be improved as well.
In addition, non-uniform angle measurement sensitivity/resolution exists over the measurement range of the femtosecond mode-locked laser autocollimator because the intensity of the output signal could change with the instability of the incident laser beam and the variation of diffraction efficiency of the grating reflector according to the tilt angle. However, this can be well solved simply by monitoring the light intensity fluctuation of the diffraction beam with a photodiode having a relatively large sensitive area through splitting the beam with a beam splitter located in front of the collimator objective that has been addressed in our previous research [15].
4. Conclusions
An optical frequency domain angle measurement method associated with a mode-locked femtosecond laser autocollimator, which can provide a higher signal visibility and improved measurement sensitivity over a large measurement range, has been proposed. A collimated laser beam from a femtosecond laser, whose optical spectrum consists of a comb of optical modes with frequencies spaced by a repetition rate over the spectrum, is modulated by a Fabry-Pérot cavity and projected onto a diffraction grating reflector. The group of the first-order diffracted beams, which have one-to-one correspondence relationship with the optical modes of the femtosecond laser, are focused by a collimator objective and detected by an optical spectrum analyzer (OSA) through a single-mode optical fiber. Differing from the traditional detection method in time or space domain which suffers from low output visibility and limited measurement sensitivity influenced by the overlapped first-order diffracted beams, the optical frequency domain angle measurement by the OSA can clearly distinguish the output curves, which are corresponding to each first-order diffracted beam, with respect to the angle change of the grating reflector in the frequency domain. In this way, both of signal visibility and measurement sensitivity are improved over the whole measurement range. A prototype of femtosecond laser autocollimator based on the optical frequency domain angle measurement method has been constructed and angle measurement experiments have been carried out to demonstrate the feasibility of the proposed method. The experimental results have verified that the proposed femtosecond laser autocollimator with the frequency domain angle measurement method can have a full signal visibility of 100% and improved measurement sensitivity over a large measurement range of 21600 arc-seconds (6 degrees), which are much better than the performance of traditional measurement method.
It should be noted that this paper has mainly focused on the proposal and verification of the frequency domain angle measurement method for improving the visibility of output signal of the mode-locked femtosecond laser autocollimator. Some engineering work needed to be carried out in the second stage of the research for applying this method to practical applications, including detailed analysis and experimental verification of the measurement resolution and accuracy, investigation of the influence of the frequency stability on the performance of the autocollimator, implementation of angle measurement by utilizing a femtosecond laser with stabilized frequency locked to a frequency standard and a stabilized Fabry-Pérot cavity, investigation of the relationship between the sensitivity and the light intensity, as well as unification of the measurement sensitivity over the measurement range, are planned in the future work.
Funding
Japan Society for the Promotion of Science (JSPS).
References and links
1. W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision engineering,” CIRP Ann.-Manuf. Technol. 64(2), 773–796 (2015). [CrossRef]
2. W. Gao, Precision Nanometrology - Sensors and Measuring Systems for Nanomanufacturing (Springer, 2010).
3. H. Schwenke, U. N. Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Ann.-Manuf. Technol. 51(2), 685–699 (2002). [CrossRef]
4. Y. Saito, Y. Arai, and W. Gao, “Detection of three-axis angles by an optical sensor,” Sens. Actuator A-Phys. 150(2), 175–183 (2009). [CrossRef]
5. W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002). [CrossRef]
6. F. Siewert, J. Buchheim, S. Boutet, G. J. Williams, P. A. Montanez, J. Krzywinski, and R. Signorato, “Ultra-precise characterization of LCLS hard X-ray focusing mirrors by high resolution slope measuring deflectometry,” Opt. Express 20(4), 4525–4536 (2012). [CrossRef] [PubMed]
7. T. Yandayan, S. A. Akgoz, and H. Haitjema, “A novel technique for calibration of polygon angles with non-integer subdivision of indexing table,” Precis. Eng. 26(4), 412–424 (2002). [CrossRef]
8. T. B. Arp, C. A. Hagedorn, S. Schlamminger, and J. H. Gundlach, “A reference-beam autocollimator with nanoradian sensitivity from mHz to kHz and dynamic range of 107.,” Rev. Sci. Instrum. 84(9), 095007 (2013). [CrossRef] [PubMed]
9. K. Ishikawa, T. Takamura, M. Xiao, S. Takahashi, and K. Takamasu, “Profile measurement of aspheric surfaces using scanning deflectometry and rotating autocollimator with wide measuring range,” Meas. Sci. Technol. 25(6), 064008 (2014). [CrossRef]
10. Möller-Werdel optical GmbH data sheet, “Electric Autocollimators,” http://www.moeller-wedel-optical.com (accessed 24April 2017).
11. W. Gao, Y. Saito, H. Muto, Y. Arai, and Y. Shimizu, “A three-axis autocollimator for detection of angular error motions of a precision stage,” CIRP Ann.-Manuf. Technol. 60(1), 515–518 (2011). [CrossRef]
12. E. Manske, G. Jager, T. Hausotte, and R. Fussl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012). [CrossRef]
13. K. C. Fan, T. H. Wang, S. Y. Lin, and Y. C. Liu, “Design of a dual-axis optoelectronic level for precision angle measurements,” Meas. Sci. Technol. 22(5), 055302 (2011). [CrossRef]
14. Trioptics GmbH, “TriAngle LASER-Electronic Autocollimator,”http://www.trioptics.com/products/electronic-autocollimators/laser (accessed 24April 2017).
15. Y. Shimizu, S. L. Tan, D. Murata, T. Maruyama, S. Ito, Y. L. Chen, and W. Gao, “Ultra-sensitive angle sensor based on laser autocollimation for measurement of stage tilt motions,” Opt. Express 24(3), 2788–2805 (2016). [CrossRef] [PubMed]
16. Y. Saito, Y. Arai, and W. Gao, “Investigation of an optical sensor for small tilt angle detection of a precision linear stage,” Meas. Sci. Technol. 21(5), 054006 (2010). [CrossRef]
17. Y. L. Chen, Y. Shimizu, Y. Kudo, S. Ito, and W. Gao, “Mode-locked laser autocollimator with an expanded measurement range,” Opt. Express 24(14), 15554–15569 (2016). [CrossRef] [PubMed]
18. S. W. Kim, “Metrology: Combs Rule,” Nat. Photonics 3(6), 313–314 (2009). [CrossRef]
19. X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Space position measurement using long-path heterodyne interferometer with optical frequency comb,” Opt. Express 20(3), 2725–2732 (2012). [CrossRef] [PubMed]
20. Y. J. Kim, Y. Kim, B. J. Chun, S. Hyun, and S. W. Kim, “All-fiber-based optical frequency generation from an Er-doped fiber femtosecond laser,” Opt. Express 17(13), 10939–10945 (2009). [CrossRef] [PubMed]
21. D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto, “Analysis of the temporal coherence function of a femtosecond optical frequency comb,” Opt. Express 17(9), 7011–7018 (2009). [CrossRef] [PubMed]
22. T. Steinmetz, T. Wilken, C. A. Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B-Lasers Opt. 96(2), 251–256 (2009). [CrossRef]
23. M. Akbulut, J. Davila-Rodriguez, I. Ozdur, F. Quinlan, S. Ozharar, N. Hoghooghi, and P. J. Delfyett, “Measurement of carrier envelope offset frequency for a 10 GHz etalon-stabilized semiconductor optical frequency comb,” Opt. Express 19(18), 16851–16865 (2011). [CrossRef] [PubMed]
24. J. Davila-Rodriguez, K. Bagnell, and P. J. Delfyett, “Frequency stability of a 10 GHz optical frequency comb from a semiconductor-based mode-locked laser with an intracavity 10,000 finesse etalon,” Opt. Lett. 38(18), 3665–3668 (2013). [CrossRef] [PubMed]
